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x^2-4x=14.5
We move all terms to the left:
x^2-4x-(14.5)=0
We add all the numbers together, and all the variables
x^2-4x-14.5=0
a = 1; b = -4; c = -14.5;
Δ = b2-4ac
Δ = -42-4·1·(-14.5)
Δ = 74
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-\sqrt{74}}{2*1}=\frac{4-\sqrt{74}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+\sqrt{74}}{2*1}=\frac{4+\sqrt{74}}{2} $
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